Solve for $x$ and $y$ using elimination. $\begin{align*}3x+4y &= 1 \\ -x-y &= 1\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $3$ $\begin{align*}3x+4y &= 1\\ -3x-3y &= 3\end{align*}$ Add the top and bottom equations. $y = 4$ Substitute $4$ for $y$ in the top equation. $3x+4( 4) = 1$ $3x+16 = 1$ $3x = -15$ $x = -5$ The solution is $\enspace x = -5, \enspace y = 4$.